Theorem 8.7 ([1]}, Theorem 1.2) 
Let \((E, \Vert \cdot \Vert )\)  be a separable Banach space and \(X\)  be a centered Gaussian element in \(E\) .
Also, let \(K_{X}\)  be the unit ball of the reproducing kernel Hilbert space of \(X\)  in \(E\) .
For \(\alpha > 0\)  and \(\beta \in \mathbb {R}\) , if there exists some constant \(c > 0\)  such that
\(\log \mathbb {P}(\left\Vert X\right\Vert _{E} \le \epsilon ) \ge -c \epsilon ^{-\alpha }\Big [\log \frac{1}{\epsilon }\Big ]^{\beta }\) 
